I think it depends on what caused or could be causing a scar, what type of scar it is and where it is.
I was injured accidentally twice on my face once by my kitty when I tried to wash grout off her paws who decided to climb my face- always clip nails in advance- and once when I opened my car door into my face by accident. The first time I took some prednisone I had left over and it pretty much stopped any scar from forming. The plastic surgeon I saw said that was the best thing to do and how did I know that. I can't remember what I did the second time but that one took longer to heal and I was more worried about a scar. I had no sign of anything from the kitty scratch and over time nothing from the car door.
I also used mederma which has onion extract. There are plenty of scar treatment gels and other treatments depending on what type of scar you have. For cat scratches I always put some bactine on immediately and that stops my allergic/inflammation reaction. I find most of my cuts heal better with antibiotic ointment and bandaids.